OLYMPIA — Gov. Jay Inslee’s office battled assertions Wednesday that a transportation-tax package should be delayed, or that a special session wasn’t even needed to get Boeing to build the 777X in Washington state.

State lawmakers in both parties, though open to extending certain tax breaks for Boeing, cast doubts about being able to reach quick agreement on a $10 billion transportation-tax package — a deal that has eluded them all year.

Inslee’s message of urgency laid out Tuesday was muddied by a summary of a letter of understanding between Boeing and the Machinists union.

The document, posted online Wednesday, says Boeing “agrees to locate the 777X wing fabrication and assembly, and final assembly of the 777X in Puget Sound” if union members approve the contract in a Nov. 13 vote.

There is no mention that lawmakers in Olympia, in the session that starts Thursday, need to do anything to make Boeing stay.

Inslee’s office pushed back hard, arguing the governor was doing what’s needed to secure the future of the state’s largest private employer. “There are other agreements and other things at play here” aside from the union document, said David Postman, Inslee’s spokesman.

“There’s zero question that both the Machinists and Boeing understand that the Legislature is an important piece of this,” he said. “It’s not just that we think that, but all the parties think that.”

For Inslee, in office less than a year, calling a special session to aid Boeing presents a test of his ability to influence lawmakers and to persuade the aerospace giant

to keep building new planes here.

Postman forwarded statements from both Boeing and the union, written Wednesday, expressing their desire for legislative action.

An email from the union said: “District 751 Legislative Director Larry Brown is leading a 10-member delegation to Olympia (Thursday) to personally lobby legislators to support the Governor’s package of 777X proposals, including the transportation plan. Any suggestion that the union thinks Legislative action isn’t necessary is simply wrong.”

The governor’s office also provided a statement from Boeing, addressed to the governor, saying: “Pursuant to our discussions this week, Boeing is committed to placing 777X final assembly and wing fabrication in the Puget Sound region.

“This commitment, however, will be solidified if the International Association of Machinists and Aerospace Workers (IAM) District 751 contract proposal is ratified in a vote by the membership next week and favorable economic incentives are implemented by the State of Washington.”

In addition to a transportation-tax package, Inslee wants the Legislature to extend existing commercial-airplane tax incentives — due to expire in 2024 — until 2040; to expand a sales-and-use tax exemption for construction of buildings used to manufacture airplanes; and to boost enrollment in aerospace fields at colleges, among other actions.

The union says the project will include new buildings totaling more than 1.5 million square feet.

Doubts about quick action on transportation began surfacing almost as soon as Inslee announced the special session.

House Republican leader Dan Kristiansen, R-Snohomish, said he was part of a conference call Tuesday between political leaders, Boeing and the Machinists union, during which it was made clear no immediate action was needed on transportation.

“The question was asked,” Kristiansen said, “to the union and Boeing: Is the transportation issue really something that needs to be taken care of to secure this?”

They responded, “Actually that’s kind of a secondary thing to us; it’s not our first priority,” Kristiansen said.

Other lawmakers in both parties said it could take weeks to put together a deal on transportation, given ongoing negotiations over issues such as whether to use sales-tax money generated by state-funded transportation projects exclusively for transportation. Currently the money goes into the general fund.

Postman rejected the suggestion that Boeing and the unions believe a transportation package is secondary, and said a deal is possible soon.